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A ladder is leaning against a wall. The top of the ladder is 999 feet (\text{ft})(ft)left parenthesis, f, t, right parenthesis above the ground. If the bottom of the ladder is moved 3\,\text{ft}3ft3, space, f, t farther from the wall, the ladder will be lying flat on the ground, still touching the wall. How long, in feet, is the ladder?

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Kalahira
The ladder is 166335 feet long. For this problem, we have a right triangle. The hypotenuse is the length of the ladder. The short leg is 999 feet long and the long leg is the length of the hypotenuse - 3. So let's make an equation to express this knowledge. 999^2 + (h-3)^2 = h^2 Expand expression 999^2 + h^2 - 6h + 9 = h^2 Subtract h^2 from both sides 999^2 -6h + 9 = 0 Add 6h to both sides 999^2 + 9 = 6h Do the squaring and adding. 998010 = 6h Divide both sides by 6 166335 = h So the ladder is 166335 feet long.

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